The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 2a^2+2 1 1 1 1 1 2a^2+2a+2 1 1 1 1 1 1 1 1 1 1 1 2a+2 1 1 1 2a^2+2 0 1 1 1 1 1 1 1 1 1 1 1 2a^2+2a 1 1 1 1 1 1 2a^2+2a 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2a^2+2a+2 1 2a+2 1 1 1 2a^2 1 1 0 1 0 1 a a^2 3a+3 a^2+3a a^2+3a+3 a^2+2a+1 2a^2+2 2a^2+3 a+2 a^2+2 1 3a^2+3a+2 2 a+3 3a 3a^2+2a+3 1 a+1 a^2+1 3a^2+2a+2 2a^2+2a+1 2a^2+a+2 3 3a^2+2a 2a^2+a+3 3a^2+2a+1 2a+2 3a^2+3a+1 1 a+3 a^2+a a^2+a+2 1 1 3a^2+1 2a^2+2a+3 3a+2 3a+1 3a^2+a 2a^2 2a+3 3a 2a^2+3a+3 2a a+2 1 3a^2+3 3a^2+3a a^2+2 a^2+2a+1 3a^2+a+3 3a^2+3a+1 2a^2+2a 2a^2+2a a^2+a+3 a^2+2a 2a^2+1 a^2 2a^2+2a+3 3a^2+2a+2 a^2+3a a^2+a+1 2a+3 2 2a^2+a+2 a^2+3a+2 a^2+a+1 3a^2+3 a^2+3a+1 a+1 2a^2 3a^2+2a+1 1 a^2 a+2 3a^2+a+2 1 a+3 a^2+a+3 0 0 1 a^2+2a+1 a 3a^2+3a+2 1 a^2+3a+3 2a^2+3a+1 a^2 3 a^2+a+3 2a^2+2 3a^2+2 a^2+2a+3 2a+1 2a^2+a+1 3a^2+a+2 3a^2+3a+3 2a^2+a 2a^2+3 a^2+3 a^2+a+2 a+2 3a+3 a^2+1 3a+2 3a^2+3 2a+2 2a+3 a^2+a+1 a^2+3a+2 3a^2+2 2a^2+3a+3 2a+2 2a^2+a+2 a^2+a 3a^2+3a+1 2a a^2+2a+1 3a^2+1 3a^2 a^2+2a+2 a^2+3 a+1 3a^2+3a+1 2a^2+2a 2a^2+a a^2+a 3 2a^2+a+3 a+3 2a^2+3a 3a^2+2a+1 3a^2+2a+2 3a^2+3a+1 1 3a^2+3a 2a^2+3a+2 a^2+2a+2 2a a^2+3a+3 3a^2+2a+3 2a^2+2a+2 2a^2+2a+3 a^2+2 a^2 3a^2 2a^2+2a+1 3a^2+a 2a^2+3a 1 2a^2 3a^2+a 1 a^2+2 3a+2 a^2+a 0 3a^2+1 2a^2+2a 2a^2+a+1 a^2+3a+1 generates a code of length 83 over GR(64,4) who´s minimum homogenous weight is 561. Homogenous weight enumerator: w(x)=1x^0+4256x^561+56x^562+224x^563+392x^564+1456x^565+3304x^566+4480x^567+4480x^568+21896x^569+392x^570+3416x^571+2240x^572+3584x^573+9744x^574+10864x^575+7553x^576+28504x^577+1288x^578+5936x^579+3752x^580+6384x^581+10920x^582+9632x^583+6790x^584+32312x^585+1848x^586+8344x^587+4368x^588+6496x^589+11872x^590+10864x^591+6678x^592+27720x^593+35x^600+21x^608+35x^616+7x^624 The gray image is a code over GF(8) with n=664, k=6 and d=561. This code was found by Heurico 1.16 in 58.2 seconds.